In a satellite telecommunications system, often called a “Satcom” system, earth stations communicate with each other via one or more repeaters in a transparent manner. The earth stations are provided with at least one modem, one frequency transposition module for each direction (for transmission, referenced Tx, and for reception, referenced Rx), one amplifier for each direction (Tx and Rx) and with an antenna, such that a transmitting station modulates the signals according to an appropriate waveform, sends signals which modulate a carrier wave ascending to the repeater, which amplifies them, transposes them and retransmits them to the ground on a descending carrier wave, a receiving station capturing the descending carrier wave in order to demodulate the signals. In order to obtain good performance at a minimal cost, the allocation of the resources used in the Satcom links must be optimized. Several criteria are involved in the performance of these links and their implementation cost. In order to increase the capacity of the network, it is possible, for example, either to increase the size of the antennas on the ground, or to increase the bandwidth (sometimes leased) of the repeater or to increase the Equivalent Isotropically Radiated Power (Puissance Isotrope Rayonée Equivalente-PIRE) at saturation of the repeater or its operational gain, each of these options also generating a corresponding additional financial cost.
The adjustment of certain elements of the communication system makes it possible to optimize the resources used. A first element to be minimized is the consumption of resources in the space segment, in other words the allocated bandwidth and the power used. A second element relates to the size of the equipment on the ground, notably the sizes of the antennas. A third element to be optimized is the setup of the modems, a good setup making it possible to increase the capacity of the system, that is to say the network spectral efficiency, referenced η. The spectral efficiency of the network is the capacity/allocated bandwidth ratio of the repeater, the capacity being the sum of the useful data rates of all the carriers which share that same allocated bandwidth of the repeater. Knowing that the modification of one of the aforesaid elements affects the connected elements, the problem of optimization of the resources used means the overall optimization of these three elements.
A system is said to be limited by power (or by bandwidth) when 100% of the power (or, respectively, of the bandwidth) available onboard is reached whereas the whole of the bandwidth (or of the power respectively) available on board is not consumed. It is known that in order to optimize the space resources, the Satcom system must neither be limited by bandwidth nor limited by power, which is equivalent to balancing the spectral consumption on board and the power consumption on board. In practice, this principle of balance naturally results in reducing the size of the antennas for a given network spectral efficiency or in increasing the network spectral efficiency for a given size of antennas. In the case of a heterogeneous set of antennas, optimization is carried out per antenna class, that is to say per group of connections sharing the same quality indicator (the “iso-QaF” class of connections will be described and the quality factor “QaF” is defined below). In order to increase the network spectral efficiency, either the capacity at constant bandwidth is increased, or the leased bandwidth on the satellite at constant capacity is reduced. It is also known that the modulation spectral efficiency is to be adapted according to the size of the antenna of the receiving stations. Notably, the following two articles published by the MILCOM can be mentioned:                Jerry Brand, “Optimizing the warfighter's non-processing satellite transponder utilization”, Military Communications Conference, 2002;        Bruce Bennett, “DVB-S2 Technology Development for DoD IP SATCOM”, Military Communications Conference, 2006.        
More generally, it is known that there is a relationship between the modem parameters and the antenna parameters, but this relationship is not simply expressed and, at present, no method of the prior art makes it possible to plan the resources to be allocated in a Satcom network simply and in an optimal manner. In general, link budget experts use iterative algorithms in which several tens of parameters (or even about a hundred of them) are involved. The experience of these experts then guides their setup choices in order to refine the allocation of the resources for each equipment of the network. The methods used by these experts are multiple, suffer from a lack of transparency and often do not make it possible to obtain the result in just a few simple operations.
As a preamble, a list of the notations used subsequently for indicating physical values is given below:                e (adimensional), the modulation spectral efficiency (not to be confused with the Naperian number in the continuation of the text, particularly when log10 e will be written);        Eb/No (in dB), the mean energy per user bit Eb over the monolateral noise power spectral density N0, at the input of the demodulator;        ΔF (in Hz), the spectral bandwidth of the channel corresponding to a modulated carrier;        D (in bps), the useful data rate transmitted on the channel;        B (in Hz), the spectral bandwidth of the repeater;        consoPW (%), the percentage used by a carrier of the power of the repeater;        consoBW (%), the percentage used by a carrier of the bandwidth of the repeater;        PIREsoldB (en dBW), the Equivalent Isotropically Radiated Power transmitted by a carrier from the earth station;        SFD (in dBW/m2), the saturation flux density of the repeater;        IBO (in dB), the back-off at the input of the repeater;        Aup (in dB), the total attenuation of the uplink;        ΔAupfs (in dB), the additional free-space attenuation of the uplink with respect to the attenuation of the sub-satellite point (the upper index corresponds to “free-space”);        Aupnfs (in dB), the attenuation and the losses out of free space of the uplink (due, for example, to rain, scintillation, clouds, gases, misalignment and to the precision of the transmitted power level);        Msys (in dB), the system margin.        